Embed Size (px)
Citation preview
J. Fluid Mech. (2006), vol. 560, pp. 449–464. c© 2006 Cambridge University Press
doi:10.1017/S0022112006000528 Printed in the United Kingdom
449
Forced laminar-to-turbulent transitionof pipe flows
By FRANZ DURST AND BULENT UNSALInstitute of Fluid Mechanics, Friedrich–Alexander Universitat Erlangen-Nurnberg,
Cauerstrasse 4, D-91058 Erlangen, Germany
(Received 25 October 2005 and in revised form 14 March 2006)
This paper presents the results of investigations into particular features of laminar-to-turbulent transition of pipe flows. The first part considers transitional flows thatoccur ‘naturally’, i.e. without any forcing, when a critical Reynolds number is reached.Measurements are reported that were carried out to study the intermittent natureof pipe flows before they become fully turbulent. The second part of the paperconcentrates on forced laminar-to-turbulent transition where the forcing was achievedby ring-type obstacles introduced into the flow close to the pipe inlet. The influenceof the ring height was investigated and the results showed a dependence of thecritical Reynolds number on the normalized height of the disturbances. The laminar-to-turbulent transition was also investigated when caused by partially closing aniris diaphragm that permitted the flow to be forced to turbulence over short timeintervals. Investigations of controlled intermittency became possible in this way andcorresponding results are presented.
1. Introduction, literature and aim of the workAt least since the famous dye experiment of Reynolds (1883), there has been
an overall understanding that fluids can flow through pipes in two distinct states,depending on the Reynolds number, Re, of the flow. Below a critical Reynolds number,the flow has the properties of a Hagen–Poiseuille flow and accidental disturbancesthat enter the flow are rapidly obliterated. The flow is referred to as being laminarand is said to be stable with respect to the introduced disturbances. As the Reynoldsnumber is increased, the flow becomes increasingly sensitive to disturbances and it isobserved that the fluid motion becomes irregular in time and space. This state of theflow is referred to as turbulent and its irregular motion at every location in the pipeis accompanied by an increase in friction factor, cf (Re). All this is well known andthe overall properties of laminar and turbulent pipe flows can be considered as beingavailable in the fluid mechanics literature.
In spite of the good knowledge of laminar and turbulent pipe flows, there arestill a number of open questions regarding details of the two flow states. Most ofthese questions relate to the regime where the flow changes from the laminar tothe turbulent state. Available studies suggest that the flow becomes turbulent at acritical Reynolds number in the range 2000–100 000 (e.g. see Schiller 1934; Ekman1883; Pfenniger 1861), depending on the ‘smoothness of the inlet’ to the pipe flow.However, this general explanation is insufficient to explain the wide range of criticalReynolds numbers found in the literature for the occurrence of transitions. No clear
450 F. Durst and B. Unsal
picture exists of what ‘smoothness of the inlet’ means and how it relates to the criticalReynolds number at which transition occurs, i.e. there is no clear picture of whatcauses the flow to go from the laminar to the turbulent state in pipe flows.
One of the most detailed studies of the laminar-to-turbulent transition of pipeflows was carried out by Rotta (1956). He performed hot-wire velocity measurementsthrough a pipe with length-to-diameter ratio L/D = 333 and he was able to keep theair flow rate constant with a specially designed air supply valve, to prevent the flow rateoscillations usually induced by pressure drop changes, at the transitional Reynoldsnumbers. With three different inlet configurations, he obtained similar transitionalReynolds numbers. In Rotta’s case, the flow was intermittent in the range 2000 � Re �3000. Mean velocity profiles and intermittency were measured at different locationsover the entire pipe length and, in this way, various details of the flow behaviouremerged.
Even more extensive work was carried out by Wygnanski & Champagne (1973),Wygnanski, Sokolov & Friedman (1975) and Rubin, Wygnanski & Haritonidis (1980).They showed the existence of two different flow structures during the laminar-to-turbulent transition of the flow, and referred to them as puffs and slugs, dependingon their occurrence and dependence on the Reynolds number of the flow. Puffs weregenerated in their experiments by large disturbances at the inlet of the pipe and existedfor the range 2000 � Re � 2700 and slugs were generated by small disturbances forRe � 3200. These authors carried out detailed hot-wire velocity measurements in anL/D = 500 pipe test rig, and it was claimed that a constant pressure drop for the airflow through the pipe was established for the investigations. The transitional Reynoldsnumber measured in the investigations of Wygnanski and co-workers varied whenthe inlet nozzle–pipe configuration was changed or when mechanical disturbanceswere applied at the inlet. They measured mean velocities and turbulence intensitiesby using conditional sampling methods and ensemble averaging techniques to yieldmean flow data. From these measurements, it was concluded that in their interiorflow structure slugs had similar characteristics to the corresponding fully developedturbulent flow. The flow structures of the observed puffs differed from these typicalcharacteristics of the fully developed state of the turbulent flow. Slugs also showeddefinite interfaces at their heads and tails. The length of a slug was of the same orderas the pipe length and in some cases its duration corresponded to a time longer thanthe passage through the pipe length. Puffs, on the other hand, did not show a clearinterface at their head, their mean velocities were roughly the same as the mean flowvelocity of the pipe flow, the length of puffs stayed, on average, constant at a givenReynolds number and their duration was in general shorter than the passage timecorresponding to the pipe length.
In investigations by Darbyshire & Mullin (1995), a constant-mass-flow-rate test rigwas used similar to that of Rotta (1956), but using water as the fluid medium.Disturbances were created by water injections with one and with six injectorconfigurations at L/D = 70 downstream from the pipe inlet. They observed similarflow structures as Wygnanski & Champagne (1973). However, the main aim of theirstudy was not the distinction of different flow structures but finding the thresholddisturbance amplitude to initiate transition. They did not observe any turbulentmotion below Re ≈ 1760. From their investigations, Darbyshire & Mullin (1995)concluded that the turbulent structures that they observed were independent of thekind of macroscopic disturbances that they applied to the flow.
In more recent studies by Draad, Kuiken & Nieuwstadt (1998) and Hof, Juel& Mullin (2003), investigated the amplitudes of the threshold disturbances yielding
Forced laminar-to-turbulent transition of pipe flows 451
Air at 5 bar
Mass flow ratecontroller
Flow conditioner
Pressure sensors
Pr1
0.03 m 2 m 1 m 2 m10 m × 15 mm
brass pipe
2 m 1 m 1 m 0.97 m
Pr2 Pr3 Pr4 Pr5 Pr6 Pr7
Hot-wire probe
Hot-wireanemometer
Oscilloscope
Amplifier
DAQ interface
Figure 1. Schematic representation of the experimental test-rig.
laminar-to-turbulent transition of pipe flows and their dependence on the Reynoldsnumber. In these studies, very similar to those of Darbyshire & Mullin (1995), periodicblowing and sucking through holes in the wall were used to disturb the flow. Thethreshold amplitudes were defined based on the injected mean flow rate. Owing todifferences in the experimental details, quantitative agreement with the results ofDarbyshire & Mullin (1995) was not obtained, as discussed by Trefethen et al. (2000).
The present investigations are based on the above-mentioned results of previousinvestigations and can be considered as an extension of the studies by Rotta (1956)and Wygnanski & Champagne (1973). The investigations were preformed with a testrig including a 15 mm diameter brass pipe, with L/D = 667. A mass flow control unitwas applied to generate constant flow rates corresponding to predetermined Reynoldsnumber. Along the pipe and over its entire length, seven pressure transducers wereinstalled, which allowed one to observe the growth and decay of the transitional flowstructures. At the exit of the pipe, hot-wire velocity measurements were conducted torecord the state of the flow. In § 2, the experimental test rig and the measurementsconducted are described. Section 3 summarizes the measurements conducted undernatural transition conditions. In § 4, the results are given for ring-type obstacles atthe pipe inlet. The results for the iris-diaphragm-triggered turbulence are summarizedin § 5, and in § 6 conclusions and an outlook for future research in this field arepresented.
2. Test rig and measuring equipmentTo carry out investigations of various aspects of laminar-to-turbulent transitions
of pipe flows, a test rig was set up with the major components shown in figure 1.Its main part consisted of a brass pipe of 15 mm diameter and total length 10 m,corresponding to L/D = 666.7. The flow of air was provided by a high-pressure supplyline connected to a mass flow rate control unit of the type described by Durst et al.(2003). This unit is shown in figure 2, providing information about the theoreticalbackground of the operation of the control valve and of its control electronics. Thisfigure provides information on all the essential parts that control the mass flow ratesupplied to the brass pipe test rig to within ±1% of the required flow. The entiresystem operates in such a way that pressure changes in the transitional flow regimedo not influence the mass flow through the pipe.
The flow rate control unit was driven by a pressure supply of 5 bar imposed in itspre-chamber. This generated a flow through a critical nozzle, providing a constant
452 F. Durst and B. Unsal
(a)
(b)
Digital input(parallel port)
Analogue in(0...10v)
Vent off
Calibration
A/D
PH PL
TL
PH
ReTH
U1(x1), T(x1)P(x1), ρ(x1)
TH
ρH ρL
High-pressurechamber
Low-pressurechamber
Valve closed Valve open
D
xRx
R
π R2
AB
R
c b
ax
drR sin �
sin 2 �1 + 2 – cos �
x2
x1 �
1κ – 1
κ + 1κ + 122κ
m =m = F (PH, TH, κ, R2, x, �)..
Status
Flow rate display
Electronic controllerfor flow ratesupply valve
Flow ratesupplyvalve
Air out0–180 1min–1
Controlunit
Figure 2. (a) Basic fluid flow considerations and relationship for m(x); (b) control circuit,actual mass flow rate controller.
2.0Re = 16980
150201003050002030
(a) (b)
1.6
1.2
0.8
0.4
0–1.0 –0.5 0
r/R Re
U/U
mea
n
u′/U
0.5 1.0 010–3
10–2
10–1
3000 6000 9000 12000 15000 18000
Figure 3. (a) Selected mean velocity profiles across the pipe and (b) centreline turbulenceintensity variation with Reynolds number at the pipe exit.
mass flow rate proportional to the nozzle area, as shown in figure 2. Pressure variationsin the pre-chamber of the mass flow rate control unit were recorded and used bythe electronics sketched in figure 2 to ensure that mass flow rate m = constant wasachieved for each set flow rate. Hence the nozzle flow area was set to achieve aconstant Reynolds number by a linear drive, as explained by Durst et al. (2003). Inthis way, the test rig, sketched in figure 1, permitted pipe flow investigations understeady flow conditions.
To provide a well-controlled inlet flow to the pipe, various flow conditioners wereapplied and the final one chosen was installed. As shown in figure 3, it permitted
Forced laminar-to-turbulent transition of pipe flows 453
the laminar flow regime of the pipe flow to be monitored up to Re ≈ 13000. Byrepeating experiments it was shown that the Reynolds number range at which thelaminar-to-turbulent transition occurred was highly repeatable within ±2% of theappropriate Reynolds number setting. Typical velocity profiles, measured at the exitof the pipe for different Reynolds number, are also given in figure 3. For the highestReynolds number, still lying in the laminar regime, the turbulence level of the flow isindicated in figure 3, showing a turbulence level of u′/U ≈ 0.2%. This turned out tobe sufficiently small to carry out the investigations described in this paper.
To carry out instantaneous pressure measurements along the pipe, seven pressuretransducers were installed, each with an operating range of ±20 mbar and 1 kHz timeresolution. The locations of the pressure transducers along the pipe are shown infigure 1 registering the occurrence of laminar or turbulent flow, at that particularlocation along the pipe, of course only with the local resolution given by theselocations. This turned out to be sufficient for the laminar-to-turbulent flow transitionalinvestigations described in this paper.
As already mentioned, a hot-wire anemometer set-up was employed at the exit ofthe pipe to carry out local velocity measurements. It included a traversing systemand a single wire probe connected to a DISA 55 M01 constant-temperature hot-wireanemometer. To obtain velocity profile measurements, the vertical motion of thetraversing system was activated and controlled through a PC. All pressure transducerand hot-wire anemometer output was connected to a 16-channel 16-bit 333 kHz dataacquisition card for simultaneous measurements of velocity and corresponding wallpressures. The output flow rate of the mass flow rate controller was also set bythe PC and a special software program ensured that the entire measurements couldbe carried out in a well-controlled manner. Various sub-programs within the dataacquisition system were written to carry out the processing of all data to yield theflow and pressure information provided in this paper.
The above-described properties of the flow control unit and the test-rig make itclear that this flow facility is ideally suited to studying transitional flows. Whenturbulent transition occurs in a pipe, the pressure drop changes and the unit, whichthe authors have built for this purpose, automatically adjusts immediately to take thisincreased pressure drop into account to yield a pipe flow with a constant mass flowrate. Wygnanski and co-workers had to achieve this by running their test-rig at highpressures so that the pressure changes due to laminar-to-turbulent transition did nothave a big effect on their results.
3. Studies of natural transitionThe test rig (figure 1) represented an ideal test section for studying the naturally
occurring laminar-to-turbulent transition. As mentioned in the previous section, initialexperiments showed that for the finally chosen inlet flow conditioner the laminar-to-turbulent transition took place at a Reynolds number of around 13000. Below thiscritical value, the turbulence intensity, at the centreline of the flow, remained below0.2%, representing the background turbulence of the test facility. With increasingReynolds numbers, the flow became intermittently turbulent, yielding instantaneousvelocity records at the end of the pipe, as indicated in figure 4. The instantaneouscentreline velocity is shown in figure 4 for various Reynolds numbers, Re � 12990,indicating the onset of intermittency for Re � 13080. The flow was fully turbulent, i.e.intermittency free, for Re � 13300. The intermittency of the flow resulted in slug-likedisturbances, as observed by Wygnanski & Champagne (1973) and Wygnanski et al.
454 F. Durst and B. Unsal
28
24
20
U (
m s
–1)
U (
m s
–1)
16
0 10 20 30
Re = 12990
Re = 13265
40 50 60
28
24
20
16
0 10 20 30Time (s) Time (s) Time (s)
40 50 60
(a)
(d) Re = 13355 (e) Re = 13450 ( f )
28
24
20
16
0 10 20 30
Re = 13080
Return tolaminar state Return to
laminar state
40 50 60
28
24
20
16
0 10 20 30 40 50 60
(b)
28
24
20
16
0 10 20 30
Re = 13170
40 50 60
28
24
20
16
0 10 20 30 40 50 60
(c)
Figure 4. Instantaneous centreline velocity plots around the transitional Reynolds numbersfor natural transition to turbulence.
1.0
0.8
0.6
0.4
Inte
rmit
tenc
y
0.2
011000 12000 13000
Re Re14000
Start of intermittent flow
Re-range ofintermittent flow
15000 16000 11000 12000 13000 14000 15000 16000
10–1 Velocityovershoot Turbulence intensity
above Recr
Turbulence intensity
below Recr
10–2u′/U
10–3
Figure 5. Intermittency at the pipe exit and corresponding turbulence intensity as a functionof Reynolds number.
(1975), consisting of time-varying flow periods with ‘jumps’ from the laminar to theturbulent flow state and vice versa.
From the intermittency function (ratio of total turbulent state duration to overallmeasurement time) of figure 5 and the corresponding turbulent intensities, as a fuctionof Reynolds number, one can see that high turbulent intensity values are measuredowing to high velocity jumps between laminar and turbulent velocity profiles asindicated in figure 4(b) and 4(c). The turbulent intensity overshoots shown for theaxial velocity fluctuation in figure 5 are due to this jump-like flow behaviour.
These velocity and intermittency measurements permit a good insight into theoverall flow structures that occurred in the Reynolds number range of laminar-to-turbulent transition, although all information was deduced from the velocitymeasurements at the outlet of the pipe. The corresponding pressure measurementsin figure 6(a) show the pressure variation with time in the Reynolds number rangewhen slugs were formed. Figure 6(b) shows the corresponding velocity signal at the
Forced laminar-to-turbulent transition of pipe flows 455
1600
1400
1200
1000
Pre
ssur
e (P
a)
800
600
400
200
042.0
t1 t3
x/D
t2
x/D = 2135
28
24
20
18
42.0 42.5 43.0 43.5 44.0
U (
m s
–1)
203336470536603
42.5 43.0Time (s) Time (s)
43.5 44.0
t1
t2
t3
Figure 6. Measured pressure and velocity waveforms of a single slug structure. The pressurewaveforms indicate the travel of a slug structure through the pipe length and the velocitywaveform shows the slug structure at the pipe exit.
end of the pipe. Looking at both time traces permits the following information to bededuced:
(i) The slug flow starts to develop from the inlet of the pipe. It is swept downstreamand fills the pipe as time proceeds. This development occurs within the time periodt1 to t2.
(ii) At time instant t2, the slug front reaches the pipe exit and at this time the sluglength in the pipe is a maximum.
(iii) In the time period from t2 to t3, the slug tail moves through pipe and leavesthe pipe at time instant t3.The combined velocity and pressure information is shown in figure 7. Figure 7(a)shows the r.m.s. values of longitudinal velocity fluctuations at the axis of the pipeas a function of Reynolds number. The corresponding local turbulence intensity ispresented in figure 7(b), showing the increase at Re ≈ 13000, when the laminar-to-turbulent transition occurs. The overshoot in the r.m.s. velocity fluctuations is clearlyvisible, caused by the laminar-to-turbulent and turbulent-to-laminar velocity jumpsthat occur at the beginning and end of the slug-like flows. Thereafter, i.e. for Re ≈13500, the region of fully developed turbulent pipe flow exists at all times with itswell-known turbulent flow properties.
This flow behaviour is also reflected by the friction factor f = 2τw/(ρ ˜U 2) thatcorresponds for Re � 13000 to the theoretically predicted relationship flam = 64/Re,as indicated in figure 7(c). For Re � 13500, the experimentally obtained friction factoris described well by the relationship fturb = 0.3614/Re1/4. It is interesting that the peakin the r.m.s. value of the longitudinal velocity fluctuation on the axis of the pipe flowdoes not result in a corresponding overshoot of the friction factor.
Overall, the experimental results described in this section clearly reveal that theexperimental test facility permitted laminar-to-turbulent pipe flows of air to beinvestigated in a well-controlled manner yielding highly repeatable results. Theseresults showed that the investigated laminar-to-turbulent flow transition apparentlyoccurred as a result of disturbances at the pipe inlet, i.e. transition always started at thepipe inlet. This phenomenon will require further experimental and theoretical studies.However, the results obtained so far are sufficient to permit the study of the forcedlaminar-to-turbulent flow transition described in the next two sections. They wereused in the investigations to distinguish between puff-like and slug-like transition
456 F. Durst and B. Unsal
(a)
(c)
(b)101
10–1
10–2
10–3
100
10–1u′
f
u′/U
10–2
10–3
0 3000 6000 9000Re
Re
Re
fturb
flam
120001500018000 0 3000 6000 9000 1200015000 18000
0 3000 6000 9000 12000 15000 1800010–3
10–2
10–1
100
Figure 7. (a) RMS velocity, (b) turbulence intensity and (c) friction factor change with Refor natural laminar-to-turbulent transition. Velocities were measured at the centreline of thepipe exit. Pressures were measured by the last two transducers.
D d h
t
% Blockage d (mm) h/t
7.5 14.427
14.23013.829
13.416
12.990
12.550
11.619
2.87
3.855.85
7.92
10.05
12.25
16.91
10
15
20
2530
40
Flow direction
D = 15 mm, t = 0.1 mm
Figure 8. Sketch showing the application the ring-type obstacles of diameter d which wereplaced at the exit of the flow conditioner and a table showing the dimensions of the rings withdifferent blockage ratios.
to turbulence. The flow structures are so distinctly different that a differentiationbetween puffs and slugs represented no problem in all phases of the investigations.
4. Transition forced by ring obstaclesIt is common practice in turbulent pipe flow research to utilize triggering devices up-
stream of the investigated flow to force the flow to become turbulent in a more definedmanner. For turbulent pipe flow, ring-type obstacles of the kind shown in figure 8 arecommonly employed. This encouraged the authors to look at such triggering devicesand to investigate their influence on the laminar-to-turbulent flow transition in pipes.Various rings were used and were mounted between the flow control unit shown infigure 1 and the inlet of the pipe. To ensure high concentricity of the inner and outerdiameters d and D of the rings, laser cutting and special machining were employed
Forced laminar-to-turbulent transition of pipe flows 457
Turbulent flow regime
Puffs
Slugs
Laminar flow regime
Reup
Relow
Re
14
12
10
8
6
4
2
02000 4000 6000 8000 10000 12000
h* = h
Uw
/ν
Figure 9. The variation of lower (Relow) and upper critical (Reup) Reynolds number withdimensionless ring-height h∗. The dashed areas correspond to the transitional regime the withslugs and puffs were indicated separately with different shadings.
to ensure that both diameters to had common centre and also to be accurate within± 10 µm. Different blockage ratios were employed, as indicated in figure 8. For eachblockage ratio, a separate set of investigations was carried out utilizing the velocityand pressure measurement facilities employed for the transition studies described in§ 3. Hence, the state of the flow in the pipe was deduced from pressure gradientmeasurements and turbulence intensity records at the end of the pipe.
The investigations carried out with different obstacles revealed that the criticalReynolds number for the laminar-to-turbulent flow transition decreased withincreasing obstacle height. This is shown in figure 9, providing a summary of thetransitional flow results.
For the flows triggered by obstacles at the pipe inlet, investigations were performedon the critical Reynolds number occurring for each obstacle. The results clearlyshowed, for both the pressure and velocity measurements, that the laminar-to-turbulent transition occurred over a small finite Reynolds number range, indicated byRelow and Reup. Figure 10 shows how extrapolated values of the turbulence intensitymeasurements to the laminar state of the flow, Relow, and to the turbulent state of theflow, Reup, were employed to define the Reynolds number range within which flowtransition occurs.
These investigations permit the critical ring obstacle height that is needed to turnthe flow from the laminar to turbulent state to be defined. Dimensional analysissuggests that the normalized height h∗ can be introduced as
h∗ =hUτ
ν(4.1)
to characterize the critical height, where h is the obstacle height, Uτ =√
τw/ρ the wallfriction velocity of the laminar flow, ν the kinematic viscosity, Umean the mean velocityof the pipe flow and D the pipe diameter. Utilizing h∗ = f (Re) in figure 9 yields aclear separation between the laminar and turbulent flow regimes of the pipe flow whentriggered by ring-type obstacles. The decrease in the normalized obstacle height with
458 F. Durst and B. Unsal
101
100
10–1
10–2
100
10–1
10–2
10–3
10–3
10–1
10–2
10–3
0 3000 6000 9000 12000 15000 18000
Relow
Relow
Reup
Reup= 4 × 10–4
Re0.772
= 0.2 Re–0.154
0%7.5%10%15%20%25%30%40%
0%7.5%10%15%20%25%30%40%
0%7.5%10%15%20%25%30%40%
u′
0 3000 6000 9000 12000 15000 18000
0 3000 6000 9000 12000 15000 18000
fturb
flam
f
Re
u′/U
Figure 10. Measured r.m.s. velocity, turbulent intensity and friction factor for ring-obstaclesat the pipe exit.
Reynolds number of the flow (abscissa) is clearly seen in figure 9. Furthermore theturbulent structures observed during the intermittent flow Reynolds number differ asthe Reynolds number increases. For intermittent flow Reynolds number below 3000puff-type turbulent structures were observed and for higher Reynolds number slug-type structures. This finding is also indicated in figure 9. Figure 11 shows examplesof centreline time records of puff and slug structures with velocity–time records verysimilar to those observed during the experiments of Wygnanski & Champagne (1973)and Wygnanski et al. (1975). The flow characteristics of these puff and slug structureswill be considered further in the next section.
Forced laminar-to-turbulent transition of pipe flows 459
Uc
(t)
Time
(a) (b)
Time
Figure 11. Centreline velocity time records as examples of (a) puff and (b) slug-typeturbulent structures.
Figure 12. Picture of the electronically controlled iris diaphragm placed at the inlet of thepipe section.
5. Forced transition by the iris-diaphragmThe results presented in § 2 made it clear that naturally occurring laminar-to-
turbulent transition occurs in an intermittent way and in these experiments thishappened at a critical Reynolds number of Rec ≈ 13000. At this Reynolds numberthe flow in the pipe starts to exist as a sequence of slugs that are produced in anuncontrolled way. Over a small Reynolds number range (see figure 4), the numberof slugs and their individual duration are increased until the fully developed stage ofturbulent pipe flow is reached.
In order to force the flow to show similar intermittent laminar-to-turbulent transi-tion at lower Reynolds number, ring-type obstacles were employed in a sequence ofexperiments as described in § 3. Depending on the height of the ring-type obstacles,the critical Reynolds number could be adjusted to be anywhere in the range 2000 �Rec � 13000. At any adjusted Reynolds number for Rec � 3500, the transition againtook place in the form of slugs that occurred in a random manner with uncontrolleddurations. Figure 10 indicates that, in principle, at a length of L/D = 666.7, thenaturally occurring and the triggered laminar-to-turbulent transitions show the samecharacteristic flow properties. Hence, ring-type obstacles are effective in controllingflow transition in pipe flows, i.e. to fix the critical Reynolds number for the laminar-to-turbulent transition of the flow.
To provide even better control of the flow that permits the time of occurrenceof turbulent slugs to be controlled, in addition to their duration, an iris diaphragmwas installed at the inlet of the pipe test section as indicated in figure 12. Using
460 F. Durst and B. Unsal
16 10
8
6
4
2
0
14
12
10
8
250
200
150
100
50
0
0 4 8 12 16 20
Vel
ocit
y (m
s–1
)Time neededto pass pipe
length
Time lengthof individual
slug Con
trol
sig
nal (
V)
VelocityControl signal
∆tL ∆tS
4 8 12 16 20Time (s)
Pre
ssur
e (P
a)
x/D
x/D = 1.93135.27202.6335.93469.27535.93602.6
Figure 13. Centreline velocity and pressure records of periodically generated slug structuresby the application of the iris-diaphragm triggering device.
the results in figure 9 the iris diaphragm could be used to provide conditions forthe laminar-to-turbulent flow transition to occur in the form of slugs and puffs atany Reynolds number in the range 2650 � Rec � 13000. Initial experiments carriedout by opening and closing the iris diaphragm confirmed this. The actual time tobring the iris diaphragm into position to represent a ring-type obstacle, i.e. to providethe required flow triggering, was adjusted to be 10 ms. This time turned out to beshort enough to produce intermittently and in a controlled manner puffs and slugsin the pipe flow, depending on the setting of the Reynolds number of the flow inaccordance with the results in figure 9. Preliminary studies confirmed that the irisdiaphragm triggering device produced turbulent slugs very similar to those obtainedin the studies described in § 3. Figure 13 shows examples of slugs produced in thisway, i.e. it shows corresponding velocity records at the end of the pipe test rig andpressure–time records along the pipe, measured for Re =5176.
The extended test rig, sketched in figure 12, enabled sequences of puffs and slugsto be generated at different frequencies and with different durations. To trigger theseflow structures, characteristic for the laminar-to-turbulent flow transition in pipes, the
Forced laminar-to-turbulent transition of pipe flows 461
2.0
1.6
1.2
0.8
0.4
0 1 2 3 4 510–3
10–2
10–1
100
1.0 1.5 2.0 2.5 3.0 3.5
0.5 1.0 1.5 2.0
4.0
r/R = 0.95r/R = 00.12
(a)
(b)
0.220.320.490.620.750.850.900.950.99
r/R = 00.280.380.480.580.680.780.850.900.950.98
0.750.450
r/R = 0.950.850.680
U/U
mea
n
2.0
1.6
1.2
0.8
0.4
0 0.5 1.0 1.5 2.00
U/U
mea
n
u′/U
10–3
10–2
10–1
100
u′/U
Time (s)Time (s)
Figure 14. Time-averaged velocity and turbulence intensity profiles of (a) a slug structure atRe = 5000 and (b) a puff structure at Re = 2850.
results in figure 9 were used to provide the appropriate size of the iris diaphragmfor each set of Reynolds number. In this way, the individual flow properties ofpuffs and slugs could be studied. The same time sequences of puffs and slugs couldbe employed to study their phase-averaged mean velocity and turbulence intensityproperties. Quantities of this kind are shown in figure 14, providing the phase-averaged mean velocity as functions of the relative time for both puffs and slugs. Thecorresponding turbulence intensity is also shown in figure 14. Information is providedfor various radial locations indicating that both puffs and slugs occupy the wholecross-section of the pipe.
The results in figure 14 are examples chosen from a large number of time records ofinstantaneous velocities for puffs and slugs. The puff structure presented in figure 14(b)corresponds to Re = 2850 and the slug structure in figure 14(a) to Re = 5000. One ofthe main differences between the flow structures of puffs and slugs is in the meanvelocity variations of the heads. Puffs show a decaying velocity profile in their headwithout the more abrupt velocity variation of the head that is typical for slugs. At thecentre of the pipe, in general puffs show higher values of the local, phase-averagedturbulent intensity.
The experimental set-up also permitted the transitional cross-sectional velocityprofiles to be constructed. These profiles are shown in figure 15 for the puff and slugflow structures analysed in figure 14.
462 F. Durst and B. Unsal
1.0
0.5
–0.5
–1.00 0.4 0.8 1.2 1.6 2.0
0
1.0
0.5
–0.5
(a) (b)
(c) (d)
–1.00 0.5 1.0 1.5 2.0
0.5 1.0 1.5 2.00.5 1.0 1.5 2.0
0
1.0
0.5
–0.5
–1.00
0
1.0
0.5
–0.5
–1.00
0
U/Umean U/Umean
r–R
r–R
t = 1.4 to 1.575 s t = 3.15 to 3.3 s
t = 0.3 to 1 s t = 1 to 2 s
Figure 15. Cross-sectional velocity profiles with times corresponding to figure 14: (a) slugat Re= 5000, laminar-to-turbulent transition, t = 1.4–1.575 s of figure 14(a); (b) slug at Re =5000, turbulent-to-laminar transition, t = 3.15–3.3 s of figure 14(a); (c) puff at Re= 2850,laminar-to-turbulent transition, t = 0.3–1 s of figure 14(b); (d) puff at Re= 2850, turbulent-to-laminar transition, t = 1–2 s of figure 14(b).
Further information about the motion of puffs and slugs through the pipe couldbe deduced from the pressure records along the pipe. Especially for the slug-likeflow structures, it was possible to track their motion because of the high-pressuregradients that they produced. From the pressure records, it was possible to deducetheir ensemble-averaged head and tail velocities, showing that the head velocity of aslug increases during its motion through a pipe. Between the last two pressure sensorsof the test section, the head and tail velocities given in figure 16 were measured andcompared with results obtained by Wygnanski & Champagne (1973) and Lindgren(1969, 1957). This readily suggests that the iris-diaphragm triggering device can beemployed to provide puff- and slug-like flow in a well-controlled manner and so areeasily accessible to detailed experimental investigations.
These investigations make it clear that the iris-diaphragm extension of the test-riglet to a flow facility that permits detailed studies of puffs and slugs because theirnatural appearance becomes deterministic, permitting transitional flow studies withhigh repeatability and reliability. Its employment is recommended for future studiesof laminar-to-turbulent transition of pipe flows forced by wall-bounded obstacles.
6. Conclusion, final remarks and outlookThe laminar-to-turbulent transition in pipe flows occurs in form of slugs that
occurred naturally in the test rig for Rec ≈ 13000. To cause slugs to occur at lowerReynolds number, ring-type obstacles were introduced into the pipe wall and at
Forced laminar-to-turbulent transition of pipe flows 463
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
2000 4000 6000 8000 10000 12000 14000Re
UHead/Umean
UT
ail/U
mea
n, U
Hea
d/U
mea
n
UTail/Umean
Lindgren (1957)Lindgren (1969)
Wygnanski & Champagne (1975)
Figure 16. Normalized head and tail velocities of slug and puff structures with Reynoldsnumber.
the pipe inlet. Changing the height of the obstacle permitted varying the criticalReynolds number at which the laminar-to-turbulent flow transition occurred throughintermittently appearing slugs. Any Reynolds number in the range 3500 � Re � 13000could in this way be selected as the critical Reynolds number. The laminar-to-turbulent transition through puffs could also be selected in the Reynolds numberrange 2000 � Re � 3500.
To provide puff- and slug-like flow structures in a more controlled way, the test-rigwas modified with an iris diaphragm. Its closing and opening were controlled bya servo-driver to produce puffs and slugs at pre-determined times for pre-selecteddurations. In this way, ensemble-averaged flow properties of puffs and slugs could bemeasured and are presented.
The iris diaphragm also permits controlled intermittency experiments where theintermittency factor can be adjusted to have any pre-chosen value between zero andone. In this way, intermittently occurring laminar and turbulent flows can be producedthat are expected to show advantages when applied to heat transfer in pipe flows.
The present work received support from the DFG (Deutsche Forchunggemeinsch-aft), through contract number DU 101/61-1 to produce the mass flow rate controlunit employed in this study. Further support was obtained through internal fundingfrom LSTM-Erlangen. These fundings are gratefully acknowledged.
REFERENCES
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow.J. Fluid Mech. 289, 83–114.
Draad, A. A., Kuiken, G. & Nieuwstadt, F. T. M. 1998 Laminar-turbulent transition in pipe flowfor Newtonian and non-Newtonian fluids. J. Fluid Mech. 377, 267–312.
Durst, F., Heim, U., Unsal, B. & Kullik, G. 2003 Mass flow rate control system for time-dependentlaminar and turbulent flow investigations. Meas. Sci. Technol. 14, 893–902.
Ekman, V. W. 1883 On the change from steady to turbulent motion of liquids. Ark. f. Math A 174,1–12.
464 F. Durst and B. Unsal
Hof, B., Juel, A. A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe.Phys. Rev. Lett. 91, 244502.
Lindgren, E. R. 1957 Arkiv Fys. 12, 1–8.
Lindgren, E. R. 1969 Propagation velocity of turbulent slugs and streaks in transition pipe flow.Phys. Fluids 12, 418–425.
Pfenniger, W. 1861 Transition in the inlet length of tubes at high Reynolds numbers. In BoundaryLayer and Flow Control (ed. G. V. Lachman), pp. 970–980. Pergamon.
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whetherthe motion of water shall be direct of sinuous, and the law of resistance in parallel channels.Phil. Trans. R. Soc. Lond. A 174, 935–982.
Rotta, J. 1956 Experimenteller Beitrag zur Entstehung Turbulenter Stromung im Rohr. Ing-Arch.24, 258–281.
Rubin, Y., Wygnanski, I. J. & Haritonidis, J. H. 1980 Further observations on transition in pipe.Proc. IUTAM Symp. Stuttgart, FRG, 1979 , pp. 19–26. Springer.
Schiller, L. 1934 Neu Berichte zur Turbulenzentwicklung. Z. Angew. Math. Mech. 14, 36–42.
Trefethen, L., Chapman, S., Henningson, D., Meseguer, A., Mullin, T. & Nieuwstadt, F. 2000Threshold amplitudes for transition to turbulence in a pipe. http://arXiv.org/abs/physics/0007092.
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in pipe. Part 1. The origin of puffs andslugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281–351.
Wygnanski, I. J., Sokolov, M. & Friedman, D. 1975 On transition in pipe. Part 2. The equilibriumpuff. J. Fluid Mech. 69, 283–304.
